In the Longest Common Factor problem, we are given two strings \(S\)  and \(T\) . We are interested in finding the largest words that is a substring of both \(S\)  and \(T\) . Charalampopoulos et al.  [1]} show how to maintain the LCF of two dynamic strings \(S\)  and \(T\)  that are going through edit operation updates with polylogarithmic time per update. In the Longest Increasing Subsequence problem, we are given an input string \(S[1\ldots n]\)  that consists of numbers. We are interested in finding the longest increasing sequence of indexes \({i_1,i_2 \ldots i_x} \subseteq [1\ldots n]\)  such that \(S[i_j] < S[i_{j+1}]\)  for every \(j\in [1\ldots x-1]\) . Gawrychowski et al.  [2]} provided an algorithm for maintaining an approximation of the LIS of a dynamic string in polylogarithmic time per update. Kociumaka and Seddighin  [3]} provided an algorithm for maintaining the exact LIS of a dynamic string with polynomial sublinear time per update. In addition to the above, the problems of finding the longest palindrome substring in a text  [4]}, [5]}, finding all the runs in a text  [6]}, approximated pattern matching  [7]}, and computing the edit distance between two strings  [8]} have all been recently investigated in dynamic settings.
